June 16, 2011

Examples of Errors in Reasoning

One common way to learn about good reasoning is to pick apart arguments by spotting errors in reasoning and applying our knowledge of epistemic principles in various contexts. In other words, we can improve our rational thinking through practice. Once we can better criticize other people’s arguments, we can learn to better criticize our own. I will describe twenty examples of poor reasoning and one example of good reasoning, but I won’t immediately explain why I think the examples use poor reasoning. Instead, my answers will be listed in a separate section. You are encouraged to think about why each of these examples are examples of poor or good reasoning before reading my answers. If two arguments are presented in an example, then consider why there are errors in the reasoning of the objection rather than the positive argument. It is possible that my answers are mistaken or incomplete, but I will defend them. It’s possible for more than one error to be made, but my focus will be on the most serious failings of each argument rather than the less serious ones. Additionally, the focus here is not on false premises or conclusions as much as poor reasoning. That’s not to say that false assumptions don’t play an important role in poor reasoning in general.

Practice problems

Example 1

All dogs are mammals.

No dogs are lizards.

Therefore, no mammals are lizards.

Example 2

Imagine that Erica and her friend Elizabeth have a conversation and Erica argues, “Abortion should be legal in the first trimester because the fetus doesn’t yet have a brain, and we don’t find the interests of creatures that lack brains to be of particular importance.” Elizabeth then responds, “Erica, your argument is probably flawed because you smoke marijuana and rob liquor stores.” Let’s assume that Erica really does smoke marijuana and rob liquor stores.

Example 3

Most people think homosexuality is immoral, therefore it probably is.

Example 4

The theory of evolution doesn’t yet explain all relevant phenomenon. For example, it’s not entirely clear how a life form can have a mind from having a brain or complex nervous system. Therefore, evolution is probably false.

Example 5

Stacy stole millions of dollars from her company, laughed about it, and tried to skip town. And she’s still smiling. We captured her and we ought to wipe that smile off her face. She ought to get the death penalty.

Example 6

We have faith that our wife won’t cheat on us, that gravity will still exist tomorrow, and that bread will still be a form of food rather than poison two seconds from now. It’s perfectly reasonable to have faith in many contexts and there’s nothing unusually offensive about having faith in God. Therefore, it’s perfectly reasonable to have faith in the existence of God.

Example 7

It’s wrong to kill innocent helpless people who aren’t in any pain including five-year-old children laughing and playing with their friends, and good people sleeping soundly in their beds. Fetuses are innocent and helpless. Therefore, abortion is wrong.

Example 8

Imagine that Tina and Jennifer have a discussion. Tina says, “There probably isn’t any life on the moon. We have seen no evidence of life there, and we’ve examined soil from the moon pretty closely.” Jennifer then replies, “But we have no proof that life isn’t on the moon because it could just be well hidden. We might as well assume that life is probably on the moon until we can prove there isn’t any.”

Example 9

Statistics show that countries that have low crime rates generally have more atheists than countries with higher crime rates. Therefore, atheists are probably less immoral than people who believe in gods.

Example 10

I don’t get sick very often whenever I take daily multivitamins, so multivitamins will probably help me avoid illness in the future.

Example 11

Either we should have a free market or communism. If we have communism, then people will lose the motivation to provide quality products and services for a fair price, and that’s a good reason to reject communism. If we have a good reason to reject communism, then we have a good reason to have a a free market. Therefore, we have a good reason to have a free market.

Example 12

It’s not usually wrong to kill insects. Insects and rats are analogous insofar as they are both living creatures. Therefore, it’s not usually wrong to kill rats.

Example 13

Imagine that Cathy and Amanda have a discussion, and Cathy says, “Men should be the leader in a heterosexual relationship because there’s often no way to resolve disagreements when there are no leaders.” Amanda disagrees and responds, “You want me to believe that men should be the leader of a relationship, but many leaders in the world are tyrants and do horrible things.”

Example 14

Imagine that Margaret and Eddie have a discussion and Margaret says, “Abortion should be legal when the pregnancy is a result of rape because she didn’t choose to do anything that would lead to a pregnancy, and we should only be responsible to another person when we choose to put ourselves in a situation where we might have control over the well being of the person.” Eddie disagrees and replies, “You want to argue that a woman who get pregnant from rape never wanted to get pregnant, so they aren’t responsible for the child, but what we want often has nothing to do with right and wrong. In this case I see no reason to think that the fact a woman doesn’t want a child could make it right to kill the child.”

Example 15

It’s wrong to refuse to hire the most qualified applicant who is black just because you don’t like black people because it’s wrong to discriminate against people using arbitrary criteria rather than relevant qualifications, and it’s wrong to refuse the most qualified applicant who is an atheist for the same reason.

Example 16

All lawyers must have a degree, therefore some lawyers must have a degree.

Example 17

Either the universe was created or always existed.

The universe didn’t always exist.

Therefore, the universe was created.

Example 18

Penny and Jill have a discussion and Penny says, “Men and women should be treated as equals because people should be rewarded and given power based on their qualifications rather than their sex, which is irrelevant to a person’s qualification.” Jill then replies, “You argue that men and women should be equals because being a woman is irrelevant to one’s qualifications, but I disagree. I think women are often more qualified to work with children than men based on my experience with women and many other people share that experience. Therefore, I don’t think men and women should be treated as equals in every situation. We should assume women are going to better at certain things than men and vice versa.”

Example 19

We have some evidence of bigfoot from footprints left in soil, and many of the footprints aren’t from any known animal. Therefore, bigfoot probably exists.

Example 20

Hansel and Gretel have a discussion and Hansel says, “I saw a ghost once, and I don’t think my experience could be explained by anything else, so I believe in them.” Gretel doesn’t believe in ghosts and responds, “But ghosts are unlikely to exist given our understanding of the universe. A being can’t have a mind unless it has a body and brain.”

Example 21

We know that all men are probably mortal because we probably would have found someone who is immortal by now if there are any. We are amazed when people live to be 100 years old or older, and we will be even more amazed to find someone who can’t die.

My answers

Example 1

All dogs are mammals.

No dogs are lizards.

Therefore, no mammals are lizards.

This argument is logically invalid because we can accept both premises and reject the conclusion. If the premises of an argument can both be true when the conclusion is simultaneously false, then it’s invalid. The argument form is the following:

All A are B.

No A are C.

Therefore, No B are C.

We can replace A, B, and C, to come up with a counterexample where the premises are true and the conclusion is false:

All dogs are mammals.

No dogs are cats.

Therefore, no cats are mammals.

Example 2

Imagine that Erica and her friend Elizabeth have a conversation and Erica argues, “Abortion should be legal in the first trimester because the fetus doesn’t yet have a brain, and we don’t find the interests of creatures that lack brains to be of particular importance.” Elizabeth then responds, “Erica, your argument is probably flawed because you smoke marijuana and rob liquor stores.” Let’s assume that Erica really does smoke marijuana and rob liquor stores.

Elizabeth’s argument is an ad hominem fallacy, which argues that an argument is flawed simply because the person who produced the argument is flawed. Everyone is flawed, but sometimes people are still able to make use of good reasoning.

The ad hominem fallacy is a more specific variety of the “red herring” fallacy because it is simply irrelevant to the argument and it is often used to distract people from the argument rather than engage in a genuine debate.

Example 3

Most people think homosexuality is immoral, therefore it probably is.

This is an example of the “bandwagon fallacy.” The fact that a belief is popular doesn’t mean it’s true or even likely to be true. For example, paganism was very popular in the past, but that doesn’t seem to give us any reason to think it’s true (or was true in the past). There are also many popular myths (false beliefs), such as the belief that cold weather gives people colds.

Example 4

The theory of evolution doesn’t yet explain all relevant phenomenon. For example, it’s not entirely clear how a life form can have a mind from having a brain or complex nervous system. Therefore, evolution is probably false.

It is true that the theory of evolution doesn’t yet explain all phenomenon, and it’s true that scientists strive to have comprehensive theories that can explain everything in the relevant domain. However, being comprehensive is an ideal that is rarely reached with perfection within science and the fact that a theory is incomplete and faces anomalies doesn’t prove a theory to be false.

This is an example of an “appeal to ignorance” fallacy because it’s assumed that if we don’t know something, then something else can be proven (or disproven). What we don’t know is rarely evidence in favor of any particular belief. If we don’t know everything about evolution, that doesn’t disprove evolution anymore than it disproves all competing theories, which fare no better than evolution. For example, creationism doesn’t explain everything either.

Example 5

Stacy stole millions of dollars from her company, laughed about it, and tried to skip town. And she’s still smiling. We captured her and we ought to wipe that smile off her face. She ought to get the death penalty.

This is an example of the “emotional appeal” fallacy because we are expected to agree with the conclusion just because we are expected to be angry at Stacy for her crime and remorselessness. Although emotions are not necessarily irrelevant to argumentation, the emotion of anger isn’t relevant enough to prove that the conclusion is true. Again, irrelevant facts used in arguments are examples of red herrings and are often used to distract us rather than engage in genuine debate.

Example 6

We have faith that our wife won’t cheat on us, that gravity will still exist tomorrow, and that bread will still be a form of food rather than poison two seconds from now. It’s perfectly reasonable to have faith in many contexts and there’s nothing unusually offensive about having faith in God. Therefore, it’s perfectly reasonable to have faith in the existence of God.

This is an example of the equivocation fallacy because the word “faith” is used in two different ways. It is true that faith seems perfectly rational in the sense that we often lack certainty. We aren’t entirely certain that gravity will still exist tomorrow, but it’s still reasonable to believe it will. However, it’s not clear that faith in God’s existence is rational in this sense. We have evidence that gravity will still exist tomorrow, but it’s not clear that we have evidence in God’s existence. Even if we do have evidence in God’s existence, it doesn’t seem to be based on tangible observation, like our evidence of our wife’s fidelity or the existence of gravity.

Again, equivocation could be taken to be a red herring fallacy because it’s merely a confusion of language and can distract us from a genuine debate. The two different uses of a word are treated as the same word when they are actually two different words. The word “faith” has two different definitions insofar as it really is two different words that both look the same. When we use the word “faith” early on in the argument it means one thing, and later on it means something else and we might as well change it to be “gaith” rather than “faith” to make it clear that two different concepts are being used.

Example 7

It’s wrong to kill innocent helpless people who aren’t in any pain including five-year-old children laughing and playing with their friends, and good people sleeping soundly in their beds. Fetuses are innocent and helpless. Therefore, abortion is wrong.

This argument is an example of the “begging the question” fallacy insofar as it assumes what it must prove—that fetuses are people. Even if it’s wrong to kill innocent people, that doesn’t prove that all fetuses are people.

Example 8

Imagine that Tina and Jennifer have a discussion. Tina says, “There probably isn’t any life on the moon. We have seen no evidence of life there, and we’ve examined soil from the moon pretty closely.” Jennifer then replies, “But we have no proof that life isn’t on the moon because it could just be well hidden. We might as well assume that life is probably on the moon until we can prove there isn’t any.”

This is an example of reversing the burden of proof, which is one way people can use the appeal to ignorance fallacy. We have no reason to think that life could be on the moon, so it seems reasonable to assume there isn’t any—and anyone who wants to assume such a thing has the burden of proof. Jennifer wants to say that there needs to be strong evidence that there isn’t any life on the moon or we can rationally assume that there is, so she blatantly changes the burden of proof to the other side. There is some evidence that there is no life on the moon, but she’s right that we could have missed something. Nonetheless, it seems clear that we have more reason to think there’s no life on the moon than to assume there is.

Example 9

Statistics show that countries that have low crime rates generally have more atheists than countries with higher crime rates. Therefore, atheists are probably less immoral than people who believe in gods.

This is an example of the “false cause” fallacy. In particular, it assumes that correlation indicates causation. The fact that two elements are commonly found together isn’t strong evidence that one element causes the other. There could be some factor to explain why countries with many atheists have low crime rates other than the assumption that atheism makes people behave themselves better. Perhaps those countries don’t have a war on drugs.

One example of when correlation doesn’t indicate causation is when a person wears their “lucky socks” because they got lucky in the past while wearing them, but the socks actually had nothing to do with being lucky.

Example 10

I don’t get sick very often whenever I take daily multivitamins, so multivitamins will probably help me avoid illness in the future.

This is an example of the anecdotal fallacy, which uses testimonial evidence; and it is one way to use a “hasty generalization” fallacy. Personal experience is often insufficient to reach conclusions because it would require us to draw extreme generalizations based on a small sample. We often draw appropriate generalizations from our experiences, but we should be careful to have sufficient evidence before drawing conclusions. Racism is often based on anecdotal evidence and hasty generalizations when someone has negative experiences with people of another race. We can’t just assume a group of people all share negative characteristics because of our bad experiences with people from that group.

Example 11

Either we should have a free market or communism. If we have communism, then people will lose the motivation to provide quality products and services for a fair price, and that’s a good reason to reject communism. If we have a good reason to reject communism, then we have a good reason to have a a free market. Therefore, we have a good reason to have a free market.

This is an example of a false dilemma fallacy, which is a failure to consider all viable options. A free market and communism aren’t our only options. There are versions of capitalism, socialism, and mixtures of the two that don’t necessarily have a free market (and aren’t communist economies). A problem with communism can’t prove that we have a reason to favor the free market because we need to compare the pros and cons of every viable economic option we have.

When we fail to consider every viable option, we are also engaging in a form of cherry-picking (the “suppressed evidence” fallacy), where important information contrary to our argument is ignored, and information favorable to our argument is emphasized.

Example 12

It’s not usually wrong to kill insects. Insects and rats are analogous insofar as they are both living creatures. Therefore, it’s not usually wrong to kill rats.

This is an example of a “false analogy” fallacy because the two things aren’t as analogous as would be necessary to draw the conclusion. It’s true that insects and rats are analogous insofar as they are both life forms, but the assumption here is that it’s not usually wrong to kill any life form. However, the state of mind of the organism could be relevant and rats are significantly more intelligent than insects are; and human beings are organisms, but it’s usually wrong to kill them (perhaps because of their intelligence). Therefore, we have cause for concern when we are told that insects are analogous to rats insofar as it’s usually not wrong to kill them purely based on the fact that they are both living creatures.

Example 13

Imagine that Cathy and Amanda have a discussion, and Cathy says, “Men should be the leader in a heterosexual relationship because there’s often no way to resolve disagreements when there are no leaders.” Amanda disagrees and responds, “You want me to believe that men should be the leader of a relationship, but many leaders in the world are tyrants and do horrible things.”

Although Cathy’s argument is flawed, my concern here is with Amanda’s response. Her response is flawed because the fact that many leaders do horrible things doesn’t help us know whether men should be the leader in heterosexual relationships or not. It could be taken to be a red herring fallacy because it lacks relevance and can distract us from having a genuine debate.

Example 14

Imagine that Margaret and Eddie have a discussion and Margaret says, “Abortion should be legal when the pregnancy is a result of rape because she didn’t choose to do anything that would lead to a pregnancy, and we should only be responsible to another person when we choose to put ourselves in a situation where we might have control over the well being of the person.” Eddie disagrees and replies, “You want to argue that a woman who get pregnant from rape never wanted to get pregnant, so they aren’t responsible for the child, but what we want often has nothing to do with right and wrong. In this case I see no reason to think that the fact a woman doesn’t want a child could make it right to kill the child.”

Again, my interest here is with Eddie’s objection. Eddie changes Margaret’s argument and objects to the new version of the argument. Margaret claimed that women who are raped never choose to do anything to become responsible for another person, but Eddie equated that with “women who are raped often don’t want to have a child.” That’s uncharitable to Margaret’s argument and it’s known as the “straw man” fallacy because he created a person made of straw to argue against rather than engaging in a genuine discussion with Margaret. The straw man fallacy is a type of red herring fallacy because it distracts us from the original argument with irrelevant claims.

Example 15

It’s wrong to refuse to hire the most qualified applicant who is black just because you don’t like black people because it’s wrong to discriminate against people using arbitrary criteria rather than relevant qualifications, and it’s wrong to refuse the most qualified applicant who is an atheist for the same reason.

No major errors in reasoning here. The argument is the following:

It’s wrong to discriminate against people using arbitrary criteria.

If we refuse to hire the most qualified applicant for being an atheist, then we are discriminating against her using arbitrary criteria.

Therefore, it’s wrong to discriminate against atheists.

This argument is valid, and some justification was given in support—we know it’s wrong to discriminate against black people and there’s no reason to think being an atheist is any more relevant for a job than being black.

Example 16

All lawyers must have a degree, therefore some lawyers must have a degree.

This is an example of the existential fallacy. This argument might be good enough in ordinary discourse, but it’s technically invalid. The premise could be taken to be equivalent to “if someone is a lawyer (right now), then she must have a degree,” and the conclusion can be taken to be equivalent to “there is at least one lawyer (right now) who has a degree.” The problem here is that the premise isn’t enough to prove the conclusion. It could be that all lawyers must have a degree, but there are no lawyers. The premise can be true and the conclusion can be false at the same time. This argument has the form “If something is X, then Y; therefore something is X and Y.” Consider the following counterexample that has a true premise but false conclusion:

If any pterodactyls exist right now, then they are reptiles.

Therefore, there’s a pterodactyl and it’s a reptile.

Of course, the argument could be good enough in ordinary discourse because we all have the assumption that there is a lawyer who exists right now. The argument is valid as long as we have that assumption.

Example 17

Either the universe was created or always existed.

The universe didn’t always exist.

Therefore, the universe was created.

This argument is valid, but the problem is that the premises are controversial and they lead us to a highly controversial conclusion—and the premises lack justification. Whenever we argue, we need to make sure to justify all of our premises, especially if they are controversial. Anyone who wants to reject the conclusion could easily reject one of the premises.

Example 18

Penny and Jill have a discussion and Penny says, “Men and women should be treated as equals because people should be rewarded and given power based on their qualifications rather than their sex, which is irrelevant to a person’s qualification.” Jill then replies, “You argue that men and women should be equals because being a woman is irrelevant to one’s qualifications, but I disagree. I think women are often more qualified to work with children than men based on my experience with women and many other people share that experience. Therefore, I don’t think men and women should be treated as equals in every situation. We should assume women are going to better at certain things than men and vice versa.”

My concern here is Jill’s objection to Penny’s argument. Jill’s objection is successful insofar as she argues against one of Jill’s premises—that sex is irrelevant to our qualifications—but rejecting that premise isn’t sufficient to reject the conclusion. Even if Penny’s argument fails, there might be some other reason we should conclude that men and women should be treated as equals. Perhaps treating them as equals is the only way to stop unfair power distributions.

This could be taken to be an example of an “appeal to ignorance” because the fact that someone doesn’t know how to reach a conclusion given a certain argument doesn’t prove that the conclusion is false.

Example 19

We have some evidence of bigfoot from footprints left in soil, and many of the footprints aren’t from any known animal. Therefore, bigfoot probably exists.

There is evidence of bigfoot, but that doesn’t mean bigfoot probably exists because the evidence isn’t sufficient to come to that conclusion. The evidence for bigfoot could be a case of misidentification, misinterpretation, or a hoax. We need to make sure our conclusions aren’t exaggerated or overly ambitious.

Example 20

Hansel and Gretel have a discussion and Hansel says, “I saw a ghost once, and I don’t think my experience could be explained by anything else, so I believe in them.” Gretel doesn’t believe in ghosts and responds, “But ghosts are unlikely to exist given our understanding of the universe. A being can’t have a mind unless it has a body and brain.”

My concern here is with Gretel’s objection to Hansel’s argument. Hansel gives an argument for ghosts and Gretel gives an argument against them, but we have no way to know who’s right from this conversation. The problem is that Gretel objects to Hansel’s conclusion, but if Hansel’s argument is sound, then the conclusion must be true. The only way we can reject Hansel’s argument and conclusion is to show (1) why the argument fails and (2) why the conclusion is false. Gretel failed to do the first step, so she isn’t yet in a position to prove that Hansel’s argument fails. This gives us reason to worry that Hansel’s conclusion might not be false after all.

Example 21

We know that all men are probably mortal because we probably would have found someone who is immortal by now if there are any. We are amazed when people live to be 100 years old or older, and we will be even more amazed to find someone who can’t die.

This argument is sufficiently good in most conversations, but it’s logically invalid—the premises can be true and the conclusion can be false at the same time. The argument is the following:

We probably would have found an immortal man by now if there are any.

Therefore, there probably aren’t any.

The argument structure is “A, therefore B.” The problem is that they are too unrelated. A counterexample would be, “The sky is blue, therefore Canada is a grapefruit.”

We can fix the argument by discovering our assumption—We haven’t found any immortal men. We can now rewrite the argument using the missing premise:

We haven’t found any immortal men.

We probably would have found an immortal man by now if there are any.

Therefore, there probably aren’t any.

It’s wrong to refuse to hire the most qualified applicant who is black just because you don’t like black people because it’s wrong to discriminate against people using arbitrary criteria rather than relevant qualifications, and it’s wrong to refuse the most qualified applicant who is an atheist for the same reason.